Details

Time bar (total: 6.3s)

sample118.0ms

Algorithm
intervals
Results
52.0ms68×body1280valid
24.0ms53×body640valid
14.0ms24×body2560valid
9.0ms32×body320valid
5.0ms62×body80valid
3.0ms17×body160valid

simplify23.0ms

Calls
1 calls:
Slowest
22.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize17.0ms

Local error

Found 2 expressions with local error:

4.0b
(log (+ x (hypot 1 x)))
0.4b
(+ x (hypot 1 x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt log-prod add-cube-cbrt add-log-exp
3×pow1 fma-def add-exp-log
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Calls
2 calls:
Slowest
9.0ms
(+ x (hypot 1 x))
7.0ms
(log (+ x (hypot 1 x)))

series304.0ms

Calls
2 calls:
Slowest
203.0ms
(log (+ x (hypot 1 x)))
101.0ms
(+ x (hypot 1 x))

simplify1.8s

Calls
17 calls:
Slowest
368.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
351.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
243.0ms
(- (+ (log (/ -1 x)) (+ (log 1/2) (* 3/32 (/ 1 (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
199.0ms
(- (+ (* 2 x) (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
193.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune409.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

13.8b
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.3b
(* x -1/6)
0.0b
(fma 3/40 (pow x 5) x)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Calls
3 calls:
Slowest
5.0ms
(* x -1/6)
0.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
0.0ms
(fma 3/40 (pow x 5) x)

series246.0ms

Calls
3 calls:
Slowest
154.0ms
(fma 3/40 (pow x 5) x)
70.0ms
(fma (* x -1/6) (* x x) (fma 3/40 (pow x 5) x))
22.0ms
(* x -1/6)

simplify1.2s

Calls
18 calls:
Slowest
201.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
190.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
163.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
161.0ms
(+ x (* 3/40 (pow x 5)))
143.0ms
(* (* (* x x) x) (* (* -1/6 -1/6) -1/6))

prune429.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

19.9b
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
12.6b
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
0.3b
(/ 1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) (* x x))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
12469×associate-/r*
10230×*-un-lft-identity
9736×add-sqr-sqrt
9520×frac-sub
9360×frac-add
9107×associate-/l*
9002×add-cube-cbrt
4922×times-frac
4762×log-div
2239×clear-num frac-2neg
2172×unpow-prod-down
2151×associate-/l/
995×prod-diff
994×swap-sqr
992×associate-*l*
990×associate-*r*
724×sqr-pow
404×distribute-lft-out
352×div-inv
334×*-commutative unswap-sqr
199×fma-neg
80×flip3-+ flip-+
22×add-exp-log difference-of-squares
18×log-prod add-cbrt-cube
9×div-exp add-log-exp
8×distribute-lft-out--
7×cbrt-undiv
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×flip3-- diff-log prod-exp cbrt-unprod flip-- associate--r+
1×pow-to-exp +-commutative sum-log sub-neg rem-log-exp pow-exp log-pow
Calls
4 calls:
Slowest
221.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
194.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
13.0ms
(/ (/ 1/8 x) (* x x))
5.0ms
(/ 1/16 (pow x 5))

series364.0ms

Calls
4 calls:
Slowest
144.0ms
(log (- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x))))
86.0ms
(- (/ (/ 1/8 x) (* x x)) (+ (/ 1/16 (pow x 5)) (/ 1/2 x)))
74.0ms
(/ 1/16 (pow x 5))
60.0ms
(/ (/ 1/8 x) (* x x))